Against two kinds of nonlinear friction observers , the analytic expression of zero ve - locity interval t based on the nonlinear model of brushless dc motor system is deduced in this paper . simulation results indicate that the system performance at low velocity can be im - proved effectively using the friction observer based on coulomb friction model 针对两种不同的非线性摩擦观测器，推导了基于无刷直流电动机非线性模型的零速度时间间隔脶解析表达式，通过仿真证实，利用基于库仑摩擦模型的摩擦观测器可以有效地改善系统的低速控制性能。
Based on the analytic analysis of the linear synchronous motor ’ s layered model , the paper deducted the composing of air gap magnetic fields and the analytic expression of levitating and advancing force . these results provide theoretic guidance not only for the analysis and measurement of the vehicle ’ s air - gap magnetic fields but also for the eatablishment of the 采用各向异性介质近似模拟齿槽区域,并引入定子和转子等效电流层的概念,建立了直线同步电机的磁场分层模型,在此基础上得到了气隙磁场的组成以及悬浮力和推力的解析表达式,为气隙磁场的分析和测量以及列车运动情况下电磁力软测量模型的建立提供了理论指导。
On the ground of mpda algorithm and the conclusion of its steady - state performance evaluation , the choice of the detection threshold becomes a matter of optimization under the condition of properly chosen detection model and hypothesis . and the analytic expression of auto - adjusted detection threshold can be deduced via approximate fitting attenuation factor derived from the conclusion of performance estimation . it presents a novel approach for the optimization of detection - tracking system 基于mpda算法及其稳态性能估计的结论，在适当选择检测模型和一定假设条件下，将自适应检测门限的选择归结为一个最优化问题，通过近似拟合性能估计结论中的衰减因子，得到了最佳检测门限自适应调整的解析表达式，为检测?跟踪系统的联合优化设计提供了一种新思路。
The analytic expression of the nonlinear control law of control variable for the upfc is obtained by using the approach of designing the nonlinear optimal controller based on the differential geometry theory . as a result , the control strategy for upfc including linear and nonlinear laws is obtained in order to adapt the nonlinear character of power system 考虑到电力系统的非线性特性，运用基于微分几何理论的反馈线性化方法，得到了upfc控制变量的非线性最优控制律的解析表达式，从而提出upfc的线性与非线性最优混合控制策略。
Hence , a numerical method , referred to as the incremental impulse method in the dissertation , is developed in chapter 2 . the method is illustrated and verified through a vibro - impacting system composed of a spring - pendulum and an oscillator , for which all the possible cases can be well analyzed in terms of analytic expressions 为解决该问题，在第二章中提出了通过冲量步进来求解斜碰撞问题的思路，即在碰撞过程中逐次施加法向冲量和相应的切向摩擦冲量，由冲量-动量(矩)定理求得系统在每一步时的状态，直到碰撞物体脱离。
This conversion is based on the analytic expression of sonic and elastic wave equation , and use the different wave field extrapolation , which is initially used in seismic migration and forward modeling . this paper introduces the easy and efficient finite - difference method to realize the conversion by comparing three different methods 论文经过对三种常规波场延拓方法( kirchhoff积分法、频率波数域法和有限差分法)优缺点的比较，采用了简单易用的有限差分方法来实现这种转换。
The paper studies the degradation rule of physical mechanical property of vulcanizate during the period of heat ageing , which involves the relationship between the property , variable temperature and time . the analytic expressions for the frictional temperature rise of the interface were presented according to the theory of heat conduction of solid when a tire slides of rolls along the road . finally , the value of temperature and pressure is used to monitor the tire ' s status 本课题针对影响汽车轮胎橡胶机械性能的温度老化模型进行了一定深度的理论研究，并进一步研究轮胎的在滑动、滚动时的温度场的数学模型，在理论上论证了温度、压力是影响轮胎行使安全性能的重要因素，并以其作为最终的监测对象。
The general situation and progress of magnetic dipole theoryresearch during recent twenty years in china were introduced briefly including magnetic dipole ; linear and strip magnetic dipoles of finite lengths ; magnetic force on a magnetic particle ; the effect of magnetizing field orientation on the revelation of defect by magnetic particles ; longitudinal magnetization of rod , tube and cuboid steel ; the relationship between the slot depth in a workpiece and magnetic leakage field ; the cause of stray magnetic pattern along base apex edges of a workpiece magnetized circumferentially ; the analytic expression for the magnetic leakage fields inside and outside the slot on the cylindrical surface of a disc ; and the effect of a needle - like magnetic medium on the magnetic force between two point magnetic charges 简述20年来中国无损检测中磁偶板子理论研究的概况和进展，主要介绍磁偶极子，有限长磁偶极线和极带，磁粉颗粒的受力，磁化场方向对磁粉显现缺陷的影响，棒料、管材和方钢的纵向磁化，工件表面沟槽深度对其引起漏磁场的影响，周向磁化时工件底棱上的杂乱显示成因，圆盘边缘柱面上沟槽内外漏磁场的解析表达式和针状磁介质对两个点磁荷间磁力的影响等。
In this thesis , studies are focused on as follows : ( 1 ) based on analyzing the general transfer - matrix , the conception of the generalized double layer soil model is proposed , and the transfer - matrix ( r ) of half - infinite elastic mass is introduce - d to the analytic expressions of stress and settlement under the uniform circular , rectangular and strip vertical loads in multi - layered soil ; ( 2 ) according to the analytic expressions of the additional stress and settlement under unifo - rm circular in multi - layered soil , rectangular and strip vertical loads , the programs are develop - ed to resolve and debugged . the results show that the programs are correct ; ( 3 ) through calculating the coefficient of additional stress on the central axis of uniform circ - ular vertical loads , under the corner point of the uniform rectangular vertical loads , and on the central axis of uniform strip vertical loads , and the settlement on the center of uniform circular vertical loads and uniform rectangular loads in double - layered soil , the characters of stress and settlement are discussed ; ( 4 ) a case , as an example , is studied with different calculation methods , such as traditional theory , fem . the results obtained are compared 本文在已有研究成果的基础上进一步开展了以下几方面的研究： ( 1 )在对层状地基传递矩阵法中的总传递矩阵分析的基础上，提出了广义双层地基模型的概念，并把半无限体的传递矩阵r引入到多层地基在圆形垂直均布荷载、矩形垂直均布荷载及条形垂直均布荷载作用下附加应力与沉降的解析式中； ( 2 )根据多层地基在圆形荷载、矩形垂直均布荷载及条形垂直均布荷载作用下附加应力与沉降的解析式，编制了程序，调试通过并验证了其正确性； ( 3 )通过对双层地基圆形垂直均布荷载中心轴线上的附加应力系数和荷载中心沉降，矩形垂直均布荷载角点下的附加应力系数和荷载角点沉降及条形垂直均布荷载中心轴线上的附加应力系数进行的计算，探讨了双层地基中的附加应力与沉降特性； ( 4 )应用本文的层状地基体系理论对一个工程实例进行了计算分析，并与传统的计算方法的计算结果和有限单元方法的计算结果进行了对比分析，结果表明利用层状地基理论计算更能反映地基中附加应力分布的实际情况。
Every result in the paper is presented through specific analytic expression , including the analytic expression of homoclinic orbit or heteroclinic orbit and its melnikov function , analytical expression of periodical track surrounding the center - type singular point within the homoclinic orbit or heteroclinic orbit and its melinkov function , the critical value when periodical m point appears , the critical value when smale horseshoes chaos appears , etc . 文中的各个结果均以具体的解析形式给出，其中包括同宿轨道或异宿轨道的解析表达式及其melnikov函数；同(异)宿轨道内围绕中心型奇点的周期轨道的解析表达式及其melnikov函数；出现周期m点的临界值；出现smale马蹄混沌的临界值等。
